1. Objective: To write an equation of a circle.
11.5 Equations of Circles
Objective: To write an equation of a circle.

2. Graphing Circles
If you know the equation of a circle, you can graph the circle by identifying its center and radius.

3. Ex. 1: Graphing a circle The equation of a circle is
(x+2)2 + (y-3)2 = 9. Graph the circle.
First rewrite the equation to find the center and its radius.
(x+2)2 + (y-3)2 = 9
[x – (-2)]2 + (y – 3)2=32
The center is (-2, 3) and the radius is 3.

4. Ex. 1 (cont.): Graphing a circle
To graph the circle, place a point at (-2, 3), set the radius at 3 units.

5. Example 2:Finding the Equation of a Circle
Circle A
The center is (16, 10)
The radius is
The equation is
(x – 16)2 + (y – 10)2 = 100

6. Example 3: Finding the Equation of a Circle
Circle B The center is (4, 20) The radius is 10 The equation is (x – 4)2 + (y – 20)2 = 100

7. Example 4: Finding the Equation of a Circle
Circle O
The center is (0, 0)
The radius is
The equation is
x 2 + y 2 = 144

8. Example 5: Graphing Circles
(x – 3)2 + (y – 2)2 = 9
Center (3, 2)
Radius of 3

9. Example 6: Graphing Circles
(x + 4)2 + (y – 1)2 = 25
Center (-4, 1)
Radius of 5

10. Assignment
Page 617
#16-23